Lech-Mumford constant and stability of local rings
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911181027934208 |
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| author | Ma, Linquan Smirnov, Ilya |
| author_facet | Ma, Linquan Smirnov, Ilya |
| contents | We study further Mumford's notion of local semistability and, in particular, show that semistable singularities are log canonical under mild assumptions. We provide many new examples of semistable and unstable singularities. More generally, we develop the theory of the Lech-Mumford constant, an invariant defined as an optimal constant in the Lech inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lech-Mumford constant and stability of local rings Ma, Linquan Smirnov, Ilya Algebraic Geometry Commutative Algebra We study further Mumford's notion of local semistability and, in particular, show that semistable singularities are log canonical under mild assumptions. We provide many new examples of semistable and unstable singularities. More generally, we develop the theory of the Lech-Mumford constant, an invariant defined as an optimal constant in the Lech inequality. |
| title | Lech-Mumford constant and stability of local rings |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2508.19893 |